A Flavor of SO(10) Unification with a Spinor Higgs

Abstract

We investigate Higgs Parity Unification-a realization of $SO(10)$ grand unification based on the Higgs Parity mechanism in which the Standard Model (SM) Higgs resides in a spinor representation. The theory has an intermediate left-right symmetric stage where the $SU(2)_R$ symmetry breaking scale is fixed by the vanishing of the SM Higgs quartic coupling. The strong $CP$ problem is solved by parity. Gauge coupling unification successfully predicts $\alpha_s(M_Z)$ to within 1%. The spinor Higgs naturally leads to a seesaw origin for SM flavor observables. We identify a novel mechanism where large mixing of third generation fermions with additional heavy vector-like fermions accounts for the anarchical nature of the PMNS matrix and the lack of hierarchy in the neutrino mass spectrum, relative to the up-quarks. A fit to quark and lepton masses and mixings, with a minimal parameter set, predicts 1) A testable relation between the top quark mass and $\alpha_s(M_Z)$ which is about $(1-2)\sigma$ from current best fit values, 2) The order of magnitude of the baryon asymmetry of the universe, via leptogenesis from second-generation right-handed neutrino decays. 3) The proton decay and the neutron EDM are likely observable in next generation experiments, and 4) A normal ordered neutrino mass spectrum where $0\nu \beta \beta$ decay and the mass of the lightest neutrino are out of reach of next generation experiments.